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ТЕХНИЧЕСКИЕ НАУКИ
Mathematical modeling of dynamics of the reactor hydrotreating hydrocarbon oils to control Nagiev H.1, Aliyeva F.2 Математическое моделирование динамики реактора гидроочистки углеводородов для управления Нагиев Г. А.1, Алиева Ф. А.2
'Нагиев Гасан Али оглы / Nagiev Hasan - доктор философии по техническим наукам, заведующий отделом, отдел вычислительной математики и информатики, Институт математики и механики Национальная академия наук Азербайджана;
2Алиева Фируза Аллахкули гызы /AlievaFiruza - диссертант, преподаватель, кафедра информатики, Бакинский государственный университет, г. Баку, Азербайджанская Республика
Abstract: using an industrial reactor of hydrotreating of motor fuels as an example dynamical features of models of systems with distributed parameters are studied. The model takes into consideration non-linear effects of absorbing hydrogen by liquid phase, adsorption, desorption and chemical reactions on the surface of a catalyst. On the basis of abundant information material of computational model experiments representing evolution of distribution functions over the longitudinal coordinate of the reactor high sensitivity of such systems to vibrational modes of control is revealed.
Аннотация: на примере промышленного реактора гидроочистки изучаются динамические характеристики систем с распределенными параметрами. Модель учитывает нелинейные эффекты поглощения на поверхности катализатора газовой и жидкой фаз, а также химические реакции. На основе многочисленных вычислительных экспериментов выявлены положительные эффекты осуществления колебательного управления.
Keywords: dynamical systems with distributed parameters, oscillating control, hydrodesulfurization process, optmization.
Ключевые слова: динамические системы с распределенными параметрами, колебательное управление, процесс гидроочистки, оптимизация.
Introduction
Dynamical systems represented by differential equations in partial derivatives constitute a class of controlled objects which are full of specific features in dynamics. Industrial systems of continuous production are usually employed in stationary conditions with stabilization of some thermal and/or concentration fields following the spatial coordinates. By prescribed integral criteria optimal modes are sought as stationary solutions of differential equations written both in time and space. Among the first researches in which attention was drawn to the possibility of attaining greater optimality from using artificially of attaining greater optimality from using artificially generated vibrations along both spatial coordinates can be mentioned papers [1-3]. Then this conception began to be used very widely [4-6]. Propagating as vibrations control actions which periodically change in time create a certain steady kind of distribution of state parameter along spatial coordinates of an object. In transient modes these distributions, analysis of nature of their evolution are the principal mechanisms of processes.
Responses of objects with distributed parameters to external actions are rather specific. At the same time, one can single out certain classes of industrial processes with characteristic features of vibrational motions. The present research was based on a model of functioning of a catalytic reactor with a stationary layer of a large-grained catalyst. As an object was chosen an industrial plant for hydrocleaning of high-sulfurous motor fuel in a continuous flow of hydrogen-containing gas and raw material. These processes are typical representations of objects with distributed parameters over the longitudinal coordinate of reactors.
A catalytic reaction of combination of hydrogen with sulfur-containing substances comprised in fuels takes place on the surface of a porous catalyst [7, 9]. Chemical processes run parallel with those of absorption of hydrogen molecules in a liquid phase, adsorption, desorption of liquid phase molecules on the surface of a catalyst [10-12].
There are facts from production practice revealing a strong influence of fluctuations in the velocity of introduction of hydrogen-containing gas on the final results of sulfur cleaning of hydrocarbons being
treated. The mentioned fact had prompted an idea about the usefulness of investigating dynamical properties of models of hydrotreating reactors in relation to output data. It was expedient to conduct the model study of non-stationary modes by varying parameters of sinusoidal change in the velocity of introducing gaseous and/or liquid phase into the reactor. The properties of one - dimensional model of chemical fractions in conditions of filtration flow of gaseous and liquid phases in the medium of a large-grained catalyst were studied. The diffusion of both phases was not taken into consideration. The search for gross kinetic parameters was chosen as the main objective. According to the chosen objective, the usefulness of introduction of effective mass-transfer parameters was chiefly in the fact that it opened the way for utilization of empirical data of production technological process.
A model of dynamics of the chief variables of hydrodesulphurization reactor state
The main simplifying assumption was taken to be the concept of allowability of the uniting into one group all sulfur-containing substances as the effective kinetic parameters of mass transfer and chemical hydrogenation reactions. Hydrogen sulfide is the product of such reactions. Due to comparatively low isothermal effect of hydro-desulfurization reaction the temperature over the longitudinal coordinate of the reactor is determined only by the temperature at the entry which is mainly influenced by a heating furnace on a raw material line.
The influence of concentration of hydrocracking products and other reactions on the partial pressure of hydrogen in the gaseous phase and on hydrogen solubility in a liquid is negligibly small. The velocity of loss in mass of raw material being treated through hydrocracking with formation of gaseous substances is not considered in the writing of differential equation.
A model with nine variables of the hydrotreating reactor state in the motionless medium of a catalyst was presented in the following form:
^^-w {-^y -/ dt Sa dx qy Pi
dy. v dy. w ^
Sj y J \ qy
at (T )•
P
= 0; i = {l-H2;2-H2S};
+ ^ wqy
dt San dx P
V j
a {T)yj-pj)+Swjkb*yj-zj0 j = {l-H2;2-RS;3-H2S};
dP l
dx S (ay +aq)
i/yvy +Yqvq ) ; (1)
- wyk {bykyH - zH ) + 2ZHZRSk0 eXP (-E / RT) = 0
dzH dt
^ - wyk (bykyRS - zRS ) + zHzRSk0 eXP (-E / RT) = 0 dzHS
dt
- wyk ^ykyH2S - zH2S )= 0
The following designations are used in the equations: S, Gn, Oy - cross-section area of the reactor as
q y
well as fractions of the section occupied by gas bubbles and liquid phase, respectively; p , p , p -partial pressures in gaseous phase of hydrogen, sulfur and hydrogen sulphide, respectively; yH, ys, yH s -concentration of the same substances in liquid phase; ZH, Z^, ZH s - specific quantity of active centers
occupied by molecules of the same substances; V , v - volume rate of introduction of gaseous and liquid
q y
phases; p - pressure in the reactor; p , p - density of substances in gaseous and liquid phases,
q y
respectively; y , y - resistance factor in filtration flow of liquid and gas; w' , CD1 k - mass transfer
coefficients for «gas-liquid» phase and «liquid-solid phase»; a (T) = K* (T) + £* ; i = 1,2 - linear approximations of temperature dependences of dissolution of hydrogen and hydrogen sulphide in liquid phase,
respectively; <jjk; j = 1,3 - coefficients of adsorption on the surface of a catalyst from liquid phase of the corresponding substances; 8 — adsorption capacity of a catalyst [g / g] ;
T, R, E, k — temperature, universal gas constant and averaged parameters of hydrodesulfurization
reactions - activation energy and pre-exponential factor.
The initial and boundary conditions are prescribed in the form:
Att = 0, pt(x,0) = pt0; y,(x,0) = y,0; zt(x,0) = zt0; at x = 0, pi(0,t) = pi0(t); yt(0,t) = ym(t); z,(0,t) = zi0(t).
The following functions are introduced with the aim of studying responses of the model to periodical control actions on the velocities of gas and liquid admission into the reactor:
Vq = Vq 0 [l + U1 sin(^it)] Vy = Vy 0 [l + u2 sin(^2t) + q] (2)
where Vq0, Vy0, U1, U2,®,®2,q — varying parameters.
Optimization of mode in the space of parameters of harmonic action on the velocity of raw material introduction
An optimization criterion of non-stationary states of a hydrotreating reactor as well as that of optimization of stationary modes is residual sulfur content of treated raw material, i. e. a quantity:
T
I (~) = J yrs (£ L)dS, T >T
(3)
where T — a certain period of observation; y^ (£, L) — a function determined from the solution of
system of differential equations (1); U — vector of function (2) parameters.
For determining the optimum mode in model experimentation one can vary a number of parameters of function (2). We have studied the influence of parameters v 0, u2, ®2 and left parameters V Q, Ux = 0 unchanged.
For each variation of vector U = {Vy0,U2,(O2}; U £Uwhere U — is a domain of varying of components of this vector values of integral (3) were computed. Fig.1 shows approximations of function (3) in
a two - dimensional area, i. e. U ( ^ = (Vy0min , Vy0max ) X (®2min , ®2max ) at two values of
vibration amplitude, U2 = 0.2 (graph(a)) and U = 0.35 (graph (b)).
An approximation of these dependences by functions of two parameters at the presented values of parameters was made:
y^ = 1.08 — 0.24v 0 —1.03® + 0.46®2; U2 = 0.2,
Vy 0 , 1*2
y^ = 1.17 — 0.29vy0 —1.1® + 0.38®2; U2 = 0.35
0
Fig. 1. Approximations oof effectivity function in a two — dimensional area y0min ' Vy0max ) ^ (^2min ' ^2max ✓
of vibration control parameters u(2) = (v0mln, vy0max ) X (®2mm, ®2max ) at:
a) tt2 = 0.2 ; 6) W2 = 0.35
The presented graph demonstrates sensitivity of effectivity index of sulfur cleaning process to parameters of change in the velocity of raw material introduction into the reactor. The variants of the computational experiment: a) and b) with different degree of visuality show the presence of minimum by frequency coordinate which is a bit displaced for different graphs. This displacement is more pronounced on the portion
corresponding to lesser values of constant component of volume rate V 0 .
Conclusion
In conclusion we will note that the conducted computational experiments on the model of hydrogenation reactor in the stationary layer of a grained catalyst have revealed a significant effect showing that the result of the process can be markedly different because of divergences in velocities of mass transfer, by absorption and adsorption. In the said model we have considered only the said physical phenomena of mass transfer, and have taken into account velocities of chemical reactions without consideration for possible effects of longitudinal diffusion believing them to be practically insignificant. We have not taken into account thermal effects of exothermic reactions either. At the same time an important conclusion was made relating to mass transfer of the considered processes which characterizes not only processes of hydrocarbon sulfur cleaning but also any chemical reactions carried out in the stationary layer of a catalyst.
References
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Structural optimization of transport systems of mining enterprises
Koptev V.
Структурная оптимизация транспортных систем горнодобывающих
предприятий Коптев В. Ю.
Коптев Владимир Юрьевич /Koptev Vladimir — кандидат технических наук, доцент, кафедра горных транспортных машин, электромеханический факультет, Санкт-Петербургский горный университет, г. Санкт-Петербург
Аннотация: в статье обосновывается алгоритм выбора вида и модели транспортной машины в структуре транспортной системы горнодобывающих предприятий. Предложены энергетические критерии сравнения их характеристик с учетом выполненной транспортной работы и транспортной услуги для формирования транспортных систем горных предприятий.
Abstract: the article explains the algorithm for selecting the type and model of the transport machinery in mining companies of the transport system structure. Proposed criteria for comparing the energy of their characteristics, taking into account the work performed by the transport and transport services for the formation of the transport systems of mining enterprises.
Ключевые слова: транспорт, машина, сравнение характеристик, модель, выбор, транспортная система, алгоритм.
Keywords: transport, car, comparing the characteristics, models, choice, transport systems, algorithms.
УДК: 622.684:622.647.2
На сегодняшний день существующий рынок предложений транспортного оборудования предлагает большее количество автосамосвалов и их моделей. Например, для открытых горных работ -автосамосвалы (более 20 фирм, с количеством моделей от единиц до нескольких десятков), автопоезда, колесные скреперы. При этом многие производители предлагают технику приблизительно одинаковой компоновки, грузоподъемности и мощности, но разной цены. Задача выбора многовариантна, а применение метода со сравнением получаемых результатов и разнородных критериев (экономических, экологических, социальных, технологических и др.) не позволяет уверенно определить лучший проект (вариант). Требуется рассматривать еще другие методы, производить имитационное моделирование, основанное на математических моделях и допущениях, привносящих свою погрешность.
Особенности разработки месторождений полезных ископаемых, влияющих на выбор как вида, так и модели применение транспорта, заключается в круглогодичной работе в условиях изменяющихся дорожных условий, постоянном перемещении погрузочных пунктов, необходимости преодоления больших уклонов при подъёме горной массы и адаптации к изменяющимся объёмам перевозок, характеристикам горной массы и многим другим.
При анализе и синтезе технических систем, в том числе и транспортных систем горного производства, формируется большое количество альтернатив, из которых выбирают оптимальные с точки зрения эффективности (предпочтительности). Большое количество неопределенностей не позволяет проектировщику однозначно назначить вид транспорта для транспортных работ при проектировании системы транспорта или выбрать модель машины при модернизации парка транспортных машин горного предприятия.
Производители транспортной техники постоянно совершенствуют свою продукцию, выпускают машины с улучшенными характеристиками, новой стоимостью и не подтвержденными эксплуатацией свойствами. В то же время производители нуждаются в определении плана выпуска новых машин и запасных узлов и уверенности, что эта техника будет востребована горной промышленностью. Им нужны оценочные показатели эксплуатационных свойств, достоверность потребности в производстве
